Equaliser for digital communications systems and method of equalisation

ABSTRACT

Equalisation of a communication channel is achieved through use of a Wiener filter frequency response mechanism that operates to transform at least a portion of a data stream generated from a plurality of space time coded (STC) symbol streams received from a plurality of transmit antenna elements into a packet spectrum. A training sequence for a channel through which the symbol streams have been sent is also transformed to a channel impulse response spectrum in order to assess the channel impulse response for the channel. The packet spectrum is equalised with the channel impulse response spectrum to produce an equalised packet spectrum in the transform domain. This is then converted into a time domain equalised data stream for recovery of originally transmitted information.

RELATED APPLICATIONS

The present application is a continuation-in-part of co-pending U.S.patent application Ser. No. 09/488,721 filed Jan. 20, 2000.

FIELD OF THE INVENTION

The present invention relates, in general, to communication systemshaving non-ideal, i.e. colored, channels that produce non-uniformchannel impulse responses. The present invention is particularly, butnot exclusively, applicable to radio frequency communication systems,including second and third generation (3G) cellular systems, in whichthere is a packetisation of data, e.g. into time slots. The presentinvention finds particular application in downstream data transmissionof CDMA-based Internet access systems, for example.

BACKGROUND OF THE INVENTION

Cellular wireless has enjoyed an extremely rapid growth from the 1980s,and there is now an almost widespread coverage of cellular radioservices in industrialised countries. In recent years there has been asimilar, albeit more rapid, growth in the demand and supply of dataservices in a wireless environment. Such data services include Internetand intranet traffic and other (principally packet-based) datatransmission schemes. Indeed, demand for the support of data servicescan be seen by the amount of e-mail retrieval arid web browsing thatalready takes place in locations such as airport lounges, hotel lobbies,company conference rooms and dedicated rooms with ports for connectionto electronic notebooks and lap top computers.

As will be appreciated, data traffic is both asymmetric in nature and isnot time critical; this contrasts with a generally uniform bandwidthdistribution in voice traffic and the requirement that voice traffic besubjected to a maximum latency for coherent information reception. Moreexplicitly, far greater data bandwidth is necessary for a wirelessaccess point to subscriber terminal (i.e. the so-called forward link ordown link) than that bandwidth required in the reverse link or uplinkdirection. The asymmetry in data communication, as will be understood,arises from the fact that the uplink is generally used to solicitinformation (e.g. web pages) as opposed to relaying data files.

Cellular subscriber handsets, whilst fundamentally providing mobility,are nevertheless used when effectively stationary which may subject thesubscriber handset (or the like) to fading conditions associated withthe channel. Facing is a dominant process that adversely affects qualityof service experienced in second generation cellular systems, such asthe frequency division multiplexed (FDM) global system for mobilecommunication (GSM). Such second generation systems often operate in atime division multiplexed (TDM) downlink transmission mode to providetime diversity which attempts to address fading. Code division multipleaccess (CDMA) systems, however, are inherently less susceptible tochannel and physical environments because spread spectrum transmissionsprovide diversity gain to mitigate adverse multipath effects likefading, with each channel in the CDMA system defined by a uniquespreading code on a frequency carrier. Information recovery from anassigned channel resource in a CDMA-based system is therefore dependentupon knowledge of the spreading code. More specifically, each channel iscomprised from a unique coded sequence of “chips” that are selected froma relatively long pseudo-random spreading sequence (typically manymillions of bits in length). A communication device has access to aninformation-bearing channel by virtue of a communication device havingparticular and detailed knowledge of a specific code that identifies thespecific bits used by the information-bearing channel.

The use of orthogonal Walsh codes for downlink transmit diversityantennas may be used to address fading and coloring of a channel throughuse of space-time transmit diversity (STTD) for non-dispersive channels;this is described in the paper “Space Time Block Coded Transmit AntennaDiversity for WCDMA” presented to the European Technical StandardsInstitute (ETSI) on 30 Oct. 1998 by Texas Instruments. Essentially, STTDprovides a linear algebraic way of resolving out symbols in a channelthrough an interleaving mechanism of CDMA code words and, moreparticularly, the use of inverted and complex conjugated versions ofinterleaved CDMA code words in a diversity path. In STTD, the length ofthe CDMA code words support a certain capability for inter-symbolrejection.

Information (such as voice, data or video) is spread across all chips ofthe spreading sequences, with the processing gain of the systemdetermined by the number of chips required to construct a single databit. Essentially, the processing gain is a ratio defined by the numberof chips required per symbol/bit (generally fixed for a secondgeneration network). In general, it is therefore better that a receiverhas a high processing gain in order that it is better able todistinguish each user signal against a background of other-usergenerated interference and system noise.

From a practical but exemplary perspective, a TDD-CDMA-based system mayexhibit a frame structure of duration ten milliseconds (10 ms). Eachframe will contain a number of slots or packets, say fifteen in total,of which at least one is usually assigned to function as a controlchannel. Dependent upon a spreading factor of the CDMA-based system (butassuming that the frame is indeed 10 ms in duration and fifteen slots inlength), each packet or slot (of duration 667 μs) is 2560 chips inlength. Each packet or slot further contains at least one (and usuallyat least two) data portion(s) and at least one training sequenceinterspersed between successive data portions. The training sequencealways contains a relatively high number of chips (e.g. five hundred andtwelve in one particular form) that can be contrasted with therelatively few chips assigned to a data symbol. The training sequence,which in essence is simply a burst of random data known to an addresseddevice, is therefore used to assess (by virtue of a cross-correlationfunction) a channel impulse response for channel equalisation purposes,with the length of the training sequence rendering it effectively immuneto degradation in the downlink path. In a particular system, a CDMA codeword, sometimes referred to as a “user symbol”, comprises a maximum of256 chips. Consequently, each slot or packet of each frame contains atotal of at least ten symbols and, possibly, hundreds of symbols with512 chips (i.e. two CDMA code words, for example) consumed as thetraining sequence. Putting this in a slightly different light, the 2048remaining chips in a slot (2560–512 chips of the training sequence)comprise a number of CDMA code words based upon an applied (and varying)spreading factor. The spreading factor (SF) typically varies between,say, one and two hundred and fifty-six, with a spreading factor ofsixteen therefore yielding one hundred and twenty-eight CDMA code words.

A high speed downlink Internet access system for nomadic users within aCDMA physical layer architecture is described in the paper “CDMA/HDR: ABandwidth Efficient High-Speed Wireless Data Service for Nomadic Users”by Paul Bender et al, Pages 70 to 77, IEEE Communications Magazine, July2000.

The use of equalisers (as opposed to RAKE receivers) in communicationdevices, e.g. handsets and the like, is commonly advocated for thirdgeneration applications since it enhances bit error rate (BER)performance and can increase spectral efficiency. The function of theequaliser is to mitigate symbol corruption induced by an imperfectchannel, with an equaliser designed to condition data such that itappears to have been passed through, optimally, a perfect channel.

Equaliser design and particularly equaliser efficiency are presentlyconstrained by processing overhead/workload. In the context of a mobiledevice, workload must necessarily be restricted because of itsassociated drain on battery power. Unfortunately, in a dispersivemulti-path channel, finite impulse response (FIR) equalisers require asignificant number of filter “taps”; with each tap representing adifferent weighting coefficient that is applied to a sample. Increasingthe number of taps improves accuracy and effectiveness of the FIRequaliser. A significant problem occurs with implementation of FIRfilters in equalisers, namely that the each sample applied to an inputof the FIR equaliser must be multiplexed by each tap. In a typicalCDMA-type system, by way of example, there are eight samples per chipand a chip rate typically in excess of 1 MHz; this results insignificant workload for a digital signal processor. Indeed, in a badtime dispersive multi-path channel environment, a seventy-tap FIR couldbe required. A truncation of the number of taps would reduce computationload but at the cost of introducing side lobes into any frequency domainrepresentation. Furthermore, if the sample rate of each tap is increasedby N-fold in order to provide a requisite degree of over-sampling, thenumber of taps required to span a certain time interval and maintain thefrequency response also increases by N-fold. Consequently, there is aresultant N²-fold increase in computation load. Thus, equaliserscontaining filters designed using straightforward FIR equalisation canbe very expensive.

With respect to equalisers and mechanism of equalisation, thesegenerally fall into one of several categories identified immediatelybelow:

(i) Cholesky factorisation of the channel impulse responseautocovariance matrix. This factorisation, which relies on matrixmanipulation, is efficient when the autocovariance matrix is stronglybanded, but this banding is only associated with low dispersionchannels. After matrix factorisation, least squares filter equations aresolved by back substitution, as usual in the Cholesky method, althoughthe processing load is dependent upon the duration of the multipathspread. The Cholesky factorisation method can also be ill-conditionedand numerically unstable and some measure of accuracy in the computationis required;

(ii) Decision feedback equalisers (DFE). These uses a combination offorward FIR filtering, a threshold decision device (such as a hardlimiter) and a feedback filter. Essentially, the feedback loop providesa mechanism that attempts to subtract echos by feeding back the channelimpulse response (CIR). However, the channel subtraction mechanismprovides error propagation problems. DFEs are commonly used in FDMAapplications, such as the US 2^(nd) generation cellular phone receiversand telephone modem equalisers.

(iii) Zero-forcing filters synthesise an FIR filter and operate toequalise channel dispersion for a finite time span about an origin. Foran n-tap FIR Filter, solving to a set of linear equations will alwaysform a weight set such that the convolution of the sample channelimpulse response H_(k) and the Wiener filter response W_(k) will have acombined impulse response which is zero at n−1 arbitrary points and hasa central unit response at k=0; and

(v) The Wiener least squares filter. This equalisation techniqueutilises a modified inverse filter which controls the white noiseresponse of the filter, ie. the undesired enhancement of thermal noisefrom the antenna. If the discrete frequency response of the channel isH_(k) and the thermal noise variance is σ², then the Wiener filterfrequency response is:

$W_{k} = \frac{H_{k}^{*}}{{H_{k}}^{2} + \sigma^{2}}$

The paper “Smart Antennas for Third Generation Mobile Radio Systems” byMartin Haardt (Siemens), Stanford Colloquium on Smart Antennas”, July1999, describes channel equalisation in terms of the Wiener filteringresponse, and explores how two or more receiving antennas can beincluded in the description of the received data. A further paper by HSari et al titled “Transmission Techniques for Digital TV Broadcasting”,IEEE communications magazine 33(2) February 1995, discusses channelequalisation in the context of the Wiener filter mechanism. STTD isincluded in the standards for 3G cellular systems in the European UMTSTerrestrial Radio Access (UTRA) system and similar systems in theAmerican CDMA2000 proposals. Consequently, it is important for theseSTTD systems efficiently to implement data recovery and equalisationalgorithms in battery powered mobile units.

In general, least squares solutions (such as (i) and (iv) above) arebetter than algebraic solutions and give better BER performance.

In a dispersive channel for space time transmit diversity (STTD), thechannel impulse response matrix, data vector and antenna signals can bewritten in block vector form, with the antenna signals related to theCIR and data vector by a block convolution operation:

${y_{2k} = {{\begin{pmatrix}Y_{0} \\Y_{2} \\Y_{4} \\\vdots\end{pmatrix}\mspace{34mu} d_{2k}} = {{\begin{pmatrix}D_{0} \\D_{2} \\D_{4} \\\vdots\end{pmatrix}\mspace{34mu} h_{2k}} = \begin{pmatrix}H_{0} \\H_{2} \\H_{4} \\\vdots\end{pmatrix}}}}\;$$y_{2k} = {\sum\limits_{\tau = 0}^{2L}{d_{2{({k - \tau})}}h_{2\;\tau}}}$

The STTD operation results in the associated equaliser having to run athalf the rate of the channel sampler; this compromises the capabilitiesof the equaliser to an extent that renders the performance of theequaliser worse than an equivalent equaliser without STTD. Furthermore,the performance of RAKE filters, when installed into the equaliser, isvery poor in any significant multi-path.

Channel equalisation to address channel imperfections therefore posesimplementation difficulties.

Joint user detection algorithms (JDAs) are usually reserved for CDMAsystems that use low spreading factors (e.g. less than 32). JDA is analgebraic solution in the receiver that counters inter-user interferencecaused by multi-path in the radio channel, typically by using matrixalgebra and linear equations. The multipath renders Walsh codesbelonging to different users non-orthogonal to an extent dependent onamplitude severity. For this reason, JDA is of interest in high-speeddata options of, for example, 3G standards where spreading factors downto four may be encountered at the highest data rates. It has beenproposed that all available Walsh codes should be used in parallel foreach user on the downlink for an asymmetric bandwidth “fat pipe” variantof the 3G standards, and under these conditions the channel equaliser orJDA is desirable. Unfortunately, a significant issue arises from thatfact that JDAs are inherently processor-intensive operations and thatJDAs are required in a handheld portable terminals in which batterydrain is roughly proportional to the instruction processing rate of theprocessor and hence to the complexity of the algorithms. As such, thereis a fundamental conflict between data recovery and effective mobileoperation, with it being desirable to attain a low DSP computation countin order to extend battery life.

SUMMARY OF THE INVENTION

In accordance with a first aspect of the invention, there is provided amethod of channel equalisation comprising: receiving a data streamgenerated from a plurality of transmit antenna elements; generating viaa fast transform a packet spectrum of at least a portion of the datastream, the packet spectrum being a transform domain representation;receiving a training sequence for a channel through which the datastream has been sent and assessing a channel impulse response for thechannel based on the training sequence; generating via a fast transforma channel impulse response spectrum in the transform domain for thechannel impulse response; equalising the packet spectrum with thechannel impulse response spectrum to produce an equalised packetspectrum in the transform domain; and converting the equalised packetspectrum into time domain equalised data for recovery of information.

Equalising the packet spectrum may further include: deconvolvingtransmitted and received data streams with respect to channel impulseresponse spectra, thereby to produce at least one equalised data stream.

Equalising the packet spectrum may also include performing a minimummean square error (MMSE) spectral ratio comparison.

Preferably, the method truncates the channel impulse response spectra tolimit processing and enhance accuracy associated with equalising thepacket spectrum.

In a preferred method, assessing the channel impulse response for thechannel based on the training sequence further includes assessing amatrix-valued channel impulse response.

The data stream may be distributed in slots across a plurality offrames, each slot including the training sequence.

Optionally, the data stream may be arranged such that a code-word levelconstruction of an STTD transmitted signal is modified to a chip-levelconstruction in which CDMA code words are interleaved at a chip levelinstead of being transmitted whole in sequence.

In another aspect of the present invention there is provided anequaliser comprising: a first input for receiving a data streamgenerated from a plurality of transmit antenna elements; a processorarranged to select a sub-slot of data from the data stream and toimplement a fast transform on the sub-slot to generate a packet spectrumfor the sub-slot of data, the packet spectrum being a transform domainrepresentation; means for storing a channel impulse response spectrumgenerated from a fast transform of a channel impulse response of achannel through which the data stream has been sent, the channel impulseresponse spectrum being in the transform domain; a least squaresspectral ratio comparator coupled to receive the packet spectrum and thechannel impulse response spectrum, the least spectral ratio comparatorhaving an output providing an equalised packet spectrum in the transformdomain; and means for converting the equalised packet spectrum into timedomain equalised data for recovery of information.

The equaliser preferably includes: means for deconvolving transmittedand received data streams with respect to channel impulse responsespectra, thereby to produce at least one equalised data stream.

A memory may store a matrix-valued channel impulse response.

In a further aspect of the present invention there is provided anequaliser comprising an input, a RAM memory block, a RAM sample block, aspectrum ratio calculator having a first input connected to the RAMsample block and a second input connected to a RAM having an impulseresponse spectrum; wherein the equaliser is operable to: receive a datastream of digital signals; fill a RAM memory block; converting thesignals by way of a fast Fourier transform operation to provide a sampleRAM block Y_(k) (packet spectrum) and providing the signals to a firstinput of an equaliser; and receive, at a second input of the equaliser,an impulse response spectrum held within the RAM, which impulse responsespectrum is a fast Fourier transform of the channel impulse response;thereby to equalise the signals whereby to provide an equalised packetspectrum which undergoes an inverse fast Fourier transform to provideequalised packet waveforms.

The equaliser may be included in a communication device, such as acellular radio or data terminal.

In an embodiment, the FFT method is applied to equalisation of SpaceTime Coded signals radiated from a number of transmitter elements andreceived at a number of receiver elements. The signals can be STTDsignals; the signals can be transmitted in time division duplex mode(TDD) or frequency division duplex (FDD) mode. The signals can be data,and/or voice signals. The method of the present invention may be appliedto least squares equalisation of transmit diversity schemes where anyform of coding is applied to digitally modulated signals from two ormore different antennas, or to the variously polarised components of oneor more transmit antennas and which are known by a variety of names,such as orthogonal code transmit diversity, code-word diversity and soon. The method of the preferred embodiments may be extended to leastsquares equalisation of Space-Time coded (STC) signals received from thetransmission of several digital data streams from two or more antennas,or polarised elements of a single or multiple antennas, to one or morereceiving antennas or polarised elements of one or more antennas, whichis employed with the aim of acquiring bandwidth expansion beyond atypical Shannon rate in a radio channel.

In accordance with yet another aspect of the invention, there isprovided an integrated chip programmed to operate in accordance with themethod of the present invention.

In generality, the present invention achieves equalisation of a channelthrough use of a Wiener filter frequency response mechanism thatoperates to transform both the received data and the channel impulseresponse into the frequency domain representations using a Fast FourierTransform (FFT). Subsequently, spectral equalisation of resultant dataspectra with a channel spectrum in the frequency domain yields atime-domain equalised packet spectrum that can be converted back intothe time domain by an inverse FFT function. Ratio comparison of the dataspectrum with the channel spectral and conversion back into the timedomain equalises the channel to appear as almost white byresolving-induced inter-symbol interference. Matrix manipulation (i.e.transformation) of STTD samples (in the form of real and imaginaryvectors) incident to a receive antenna allows FFT processing of encodeddata, initially presented on either a chip-wise or symbol-wise basis inan information slot or packet. The matrix manipulation defines a set ofsamples seen at the receive antenna in terms of both a complexmultiplexed transmitted sample sequence sent from a plurality of sourcesacross separate paths that are affected by respective channel impulseresponses. The principle of applying Fourier transformation techniquesin equalisation is also applicable to systems employing multipletransmit elements and multiple receiver elements, such as in space-timecoding (STC) schemes.

The present invention advantageously provides an improved method ofequalisation and an associated equaliser for digital communicationsystems which use a number of coherent transmitter elements to achievespace-time transmit diversity (STTD) or an overall bit rate increase inspace time coding. Beneficially, according to a preferred embodiment ofthe present invention, every data chip is passed through the channelimpulse response. The mechanism underlying the preferred embodiments ofthe present invention is also, in general, a technique that enhancesperformance of the forward link in “fat pipe” CDMA systems, such asproposed to extend IS-95 CDMA base stations towards and into thirdgeneration cellular systems.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the present invention will now be describedwith reference to the accompanying drawings, in which:

FIG. 1 shows a basic CDMA transmitter and receiver architecture;

FIG. 2 is a diagrammatic illustration of a fast Fourier transform (FFT)channel equalisation technique and architecture according to a preferredembodiment of the present invention;

FIG. 3 is a diagrammatic illustration of a channel impulse responseestimation process and architecture of a preferred embodiment of thepresent invention, the channel impulse response estimation processpreferably used in relation to FIG. 2;

FIG. 4 compares a RAKE STTD equaliser structure with an FFT equaliser ofthe present invention;

FIG. 5 shows a layout of channel impulse response in {tilde over (C)};and

FIG. 6 shows the high level architecture of the wireless data system inwhich the present invention may be employed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

There will now be described by way of example the best mode contemplatedby the inventors for carrying out the invention. In the followingdescription, numerous specific details are set out in order to provide acomplete understanding of the present invention but may be put intopractice with variations of the specific.

Referring now to FIG. 1, there is shown a basic CDMA transmitter andreceiver architecture 10. Transmit and receive chains 100, 101 may becombined in a transceiver arrangement of a station, such as a basestation/Node B or a mobile device of a cellular radio system or thelike. The transmit and receive chains could, of course, be implementedin isolation, whereby unidirectional (as opposed to bi-directional)communication is supported across, for example, an air-interface.

In transmit chain 12, signal source 102 generates signals 104 which areencoded by encoder 106, such as a half rate turbo coder. Encoded signals107 signals are modulated and subjected to CDMA spreading bymodulator/spreader 108 and then filtered by digital filter 110.Following filtering, a digital to analog (D/A) converter is arranged toproduce analog signals 114 which are generally filtered in a secondfilter 116 to limit an aliasing effect at transmission. A mixer 118up-converts baseband signals 120 to transmission frequencies prior toamplification in power amplifier 122 and transmission from antenna 124.Of course, as will be appreciated, some of the functional blocks in thetransmit chain can be realised as discrete or collocated into a singlechip or processing block.

Transmitted signals 126 are received by receive antenna 128 of anaddressed station. Received signals 130 are communicated to adown-converting mixer 132 via an amplifier 134, which down-convertingmixer typically produces an intermediate frequency signal for initialsignal processing. A filter 134 isolates a desired frequency spectrum136 for signal processing, which frequency spectrum is converted to adigital domain representation 137 by analog to digital (A-D) converter138. The digital domain representation 137 is digitally filtered indigital channel filter 140 and then applied in series to a combineddemodulator/equaliser slicer and RAKE despreader 142 and then a channeldecoder 144. Recovered information 145 is ultimately received byterminal receiving equipment (TRE) 146. It will be understood thatchannel filtering generally distorts reflections in the channel responsein the time domain; resulting side lobes in the filter response maytherefore complicate processing, but this will be understood by theskilled addressee.

The transmit and receive chains 100, 101 are invariably processorcontrolled operations. By way of illustration, a controller 150 andassociated memory 152 (which may be a combination of random access (RAM)and read only (ROM)) is shown as being common to both the transmit andreceive chains 100, 101. The memory 152 stores control algorithms, suchas equalisation and modulation algorithms, and also operands andincident data is subject to signal processing requirements. Furthermore,FIG. 1 can be adopted to support the underlying principles of thepreferred embodiments of the present invention. Moreover, commoncircuitry between the transmit and receive chains can be shared toreduce component count, subject to the inclusion of suitable switchingand regulating circuitry. Additionally, as will be understood, at leastsome of the functions within one or both of the transmit and receivechains 100, 101 can be implemented either entirely or partially as code,e.g. equalisation and demodulation.

CDMA-specific components can be replaced or substituted to support anarbitrarily selected communication protocol, e.g. an FDD environmentemploying TDM techniques.

FIG. 2 is a diagrammatic illustration of a fast Fourier transform (FFT)channel equalisation technique and architecture 200 according to apreferred embodiment of the present invention. For the sake ofexplanation only, a preferred embodiment will be described in thecontext of a CDMA-based system.

Incoming signals 126 are received from the antenna 128 at a transmissionrate of ¹/T_(ch) of the system. The incoming signals are sampled into asub-slot 202 of encoded data, the sub-slot being of arbitrarily selectedlength but preferably commensurate with a length assigned to a trainingsequence within each slot of each frame. Of course, the sub-slot couldbe of shorter or longer duration than the length (in chips) of thetraining sequence, but this is a design option. By way of practicalimplementation, an entire slot of a frame is sampled (AID conversion) atthe Nyquist rate and read into memory 152 prior to commencement ofinformation recovery, with equal data field sub-slots 202 (in terms ofchip length) broken out from the stored slot or packet. The incomingsignals 126 can be received from any digital source of signals and arenot restricted to wireless communications.

From a processing perspective, it is preferred that the sub-slot 202 isactually extended beyond a data field 203 of arbitrarily selected length204, the sub-slot therefore including a packet (or sub-slot) overlapfield 206 of length τ chips. In other words the overlap field 206pertains to multi-path. The overlap field 206 is, more specifically,designed to address interference (e.g. echos) from adjacent chips orsymbols. An overall length of the overlap field is therefore at least aslong as the greatest expected channel impulse response (CIR) duration(presently understood to be seventy-one chips in length), althoughadditional redundancy/tolerance may be preferred to support systemdevelopment or refinement. The overlap field 206 is used to predictinterference in a succeeding sub-slot, which interference results fromsymbol/chip echo, with the overlap field subtracted from the succeedingsub-slot to ensure isolation of data in that succeeding sub-slot.

With respect to a first processing chain associated with a data spectrumas opposed to channel response spectrum, the sub-slot 204 (containingthe data field and the overlap 206) is converted into a frequency domainrepresentation, termed a “packet spectrum” 210, in a fast Fouriertransform (FFT) function 212. The FFT function 212 may be performed by aspecific digital signal processor (DSP) or the processor 150 of FIG. 1.The packet spectrum 210 therefore assumes the form of an x-point, e.g.512-point, FFT sample stored temporarily in RAM.

Before continuing with the description of FIG. 2, it is best to considergeneration of a “channel spectrum” according to a preferred embodimentof the present invention; this is shown in FIG. 3. A training sequence250, preferably located in and extractable from each slot of a frame,falls incident or receive antenna 128, which training sequence isdemodulated in the receive chain (as will be readily appreciated) torecover the random sequence y_(k,) e.g. a generated pseudo-random numbersequence. The recovered random sequence y_(k) is subjected to a FFTfunction 252 (in a similar way to that previously described for thesub-slot) to produce a channel sequence spectrum Y_(k) 254. Within thememory 152 associated with the receive chain there is stored a replicaof the original training sequence s_(k) 260, which original trainingsequence S_(k) 260 has a corresponding known sequence spectrum s_(k) 262obtained by subjecting the original training sequence S_(k) 260 to anFFT function. The known sequence spectrum S_(k) 262 may simply be storedin the memory since it is this sequence spectrum S_(k) 262 that is usedto assess the channel impulse response.

It will be noted that the frequency domain sequence spectrum S_(k) 262is essentially flat with slight perturbations about a nominally constantmagnitude. The sequence spectrum S_(k) 262 is compared with the channelsequence spectrum Y_(k) 254 in a cross-correlation function 266, such asrealised by Wiener filter frequency response, namely

${W_{k} = \frac{H_{k}^{*}}{{H_{k}}^{2} + \sigma^{2}}},$thereby to produce an impulse response spectrum H_(k) 268 that can bestored in memory for the duration of at least the related slot andlonger if desired. Clearly, by storing the impulse response spectrumH_(k) 268 for an extended period, processing overhead is reduced at theexpense of accuracy in any correction of the variations in the channel.As will be understood, time alignment of the received and transmittedtraining sequences is required prior to cross-correlation.

Optionally, the impulse response spectrum H_(k) 268 is further refinedand so is subjected to an IFFT function 270 to generate an estimatedtime domain representation h_(k) thereof having an arbitrary number oftaps/channels that can be used as a matched filter, if desired. In otherwords, each tap is representative of a weight for the channel impulseresponse. Within the time domain, trimming of the number of taps reducesthe channel impulse response to manageable processing levels, with thereduction reflecting the greatest expected channel impulse response(CIR) duration (presently understood to be seventy-one chips in length,although this number is an arbitrarily selected cut-off). From thereduced number of taps in the channel impulse response, most values willapproximate to zero and so a control processor 272, based on a level ornumber threshold, selects only those N significant taps that mostnoticeably reflect the channel to produce a best estimate channelimpulse response h′_(k) 274. Selection of the N most significant tapsmay simply force lesser taps to be forced to zero. By limiting thechannel impulse response to the most significant taps, processing isreduced and a final error in the channel limited. In the latter respect,it will be understood that all tap values will have an associated errorfrom thermal noise, channel interference and other adverse channel andprocessing artefacts, so the compounding of errors is mitigated.

Returning now to FIG. 2, the packet spectrum 210 is compared, typicallypoint by point, to the impulse response spectrum h′_(k) 274 (or h_(k)270, if preferred) in a minimum mean square error (MMSE) spectral ratiocomparator 290 to generate an equalised packet spectrum 292. The MMSEspectral ratio comparator 290 preferably satisfies the Wiener filterfrequency response, namely

$W_{k} = {\frac{H_{k}^{*}}{{H_{k}}^{2} + \sigma^{2}}.}$

In the multiple receive antenna element case, least mean squares (LMS)interference cancellation in the equaliser 290 is possible bypre-whitening with N×N interference matrices.

In generality, it will now be appreciated that when the data channelF(ω) is divided by its own channel spectrum H(ω) then a resultant packetspectrum is a whitened version of the data channel F(ω). In other words,a ratio of the data spectrum to the channel spectrum compensates thedata spectrum of a non-white channel by conditioning data such that thedata appears to have passed through a perfect channel. Clearly, if thechannel is non-dispersive, then the correlation between the sequencespectrum S_(k) 262 and the channel sequence spectrum Y_(k) 254 yields anull result for the CIR and no correction is applied by MMSE spectralratio comparator 290. However, with multi-path in a dispersive, i.e.imperfect, channel, each sample (whether it is a chip or symbol) willgenerate a replica of the channel impulse response in the frequencydomain, which replica can be corrected by the present invention throughthe application of a comparison function before conversion back into thetime domain for data recovery. In overview, in contrast with existingand proposed joint detection algorithms (JDAs) that address multi-pathin, for example, low spreading factor CDMA systems, the preferredembodiment of the present invention use a least squares Fast FourierTransform deconvolution operation which is much simpler to implement.Equalisation can be performed at the symbol rate for QAM modulation orchip rate for CDMA.

The equalised packet spectrum 292 is applied to an IFFT function toprovide an equalised packet (e.g. CDMA) waveform 296 in the time domain.The equalised packet waveform will include a small signal portion 298 ofthe overall waveform that will cause echo in a contiguous sub-slot,which small signal portion 298 can be tagged and temporarily stored inmemory 152 for use in intersymbol interference cancellation in animmediately succeeding sub-slot, e.g. by a processor-controlled directsubtraction mechanism from the front-end of the immediately succeedingsub-slot. The equalised packet 296, in the case of CDMA, is applied to adespreading function 300 to attain a symbol rate 1/T_(s) of the system(where T_(s)=T_(ch) /spreading factor). The despreading function 300 canbe realised by a matched filter. A decoder/quantiser 302, such as aneight or sixteen bit QAM decoder or a phase-shift keyed (PSK) decoder,is responsive to the symbol rate 1/T_(s) to recover the original data304.

The preferred embodiment of the present invention can operate on signalstransmitted in slotted time frames or otherwise on a bit-, chip- orsymbol-wise basis.

In terms of processing overhead, if we assume a 256-point FFT to supporta symbol packet of, say, one hundred and ninety-two chips, then theequalisation technique of the present invention is equivalent to a256-tap FIR, albeit that DSP workload to support the FFT function is twolog₂(256)-tap filters, i.e. a relatively small fraction of theprocessing required in the equivalent digital filter. Furthermore, DSPload is independent of channel impulse response duration, wherebyvehicular channels pose no particular problems. Use of the presentinvention provides an improved symbol-to-noise ratio for high powerratio (E_(b)/N₀), i.e. any system employing the FFT technique of thepreferred embodiment is better able to address inter-symbol (orintercode) interference (ISI).

The capabilities of the single channel equaliser are next expanded in afurther embodiment of the present invention to cover the cases ofmultiple transmitter elements and at least one receive element, such asin STTD and STC. Space time transmit diversity (STTD) has beenrecommended for dual transmit antenna elements for the third generationcellular system (see 3GPP Standards document TS25.211, “Physicalchannels and mapping of transport channels onto physical channels”.1999). Further elaboration to systems with more than two elements isdiscussed in 3GPP TSG RAN discussion document R1-00-0683_Txdiversity.doc, Samsung, “Further simulation results of Tx diversity formore than 2 antenna”. More advanced applications in space time codingfor bandwidth expansion and block coding methods compatible with the FFTequalisers of the preferred embodiments of the present invention arediscussed by Tarokh et. al. “A. R. Space time block codes fromorthogonal designs”, IEEE Trans. Information Theory, 45(5) July 1999 pp.1456–1647.

For completeness, it will be appreciated that STC is a collection oftechniques for transmitting a number of parallel data streams frommultiple transmit antennas with the aim of increasing bit rate for agiven total transmitter power. In STC, it will be appreciated that the2×2 frame structure is expanded to an N-element array, usually having atleast four transmit elements. For example, in a four element STCtransmitting antenna we might organise the user data in blocks of foursymbols and transmit them in different order from the four elements via16 channels to 4 receiving elements. This is a natural extension of thetwo element STTD procedure, the main difference from STTD being thatmultiple receiving elements are essential to get a bandwidth expansionin STC whereas STTD is aimed purely at improving the reliability of thereceived data and is not concerned with bit rate expansion. Thus STTDwill function with a single receive antenna, while STC requires aminimum of two. The processing techniques underlying Eqn. (1) to Eqn.(9) below can be expanded to address the case of more than two transmitelements communicating to at least two receive antenna elements. Theprinciple difference between the exemplary STTD arrangement (that isdiscussed in detail below) and STC is that each component of the blockvectors and block matrices (for STTD given below) contains an increasingnumber of element (i.e. CIR samples, transmitted data samples andreceived data samples) consistent with the adopted coding method in eachSTC derivative.

FIG. 4 compares a RAKE STTD equaliser structure 400 with an FFTequaliser 402 of a preferred embodiment of the present invention. STTDsignals 404, 405 are generated in and transmitted from multi-elementtransmitter 406. The S)TTD signals 404, 405 are incident to antenna 128which feeds FFT-based equaliser decoder 402 (in the preferredembodiment) or RAKE STTD decoder 400 (in the prior art). As can be seen,the RAKE STTD receiver 410 requires time aligned parallel inputs andhence a time delay for a clocking period of 2; this contrasts with thedirect coupling of the received signals into the FFT/Matrix MMSEequaliser DSP of the preferred embodiment. The RAKE STTD decoder 400contains parallel paths each containing a RAKE equaliser 414, 416 thatfeed recover paths having assumed perfect channel gains for channelimpulse responses h₁, h₂. As will be understood, and as shown (but notdescribed in detail for the sake of brevity), conjugated and, asnecessary, inverted versions of the specific channels are summed torecover data sequences S₁ and S₂.

In one embodiment of the invention, the FFT domain equalisation methodof the present invention is extended to least squares reception ofSpace-time Transmit Diversity (STTD) modulated signals as describedbelow; the technique removes inter symbol interference (ISI) andinter-code interference.

By way of illustration of the underlying principles of a preferredembodiment, in a standard STTD situation, the base station has twotransmitting antennas and the addressed subscriber unit a singlereceiver antenna element. Given a baseband modulator simpler inputsequence s₁, s₂, s₃, s₄, s₅, . . . , the base station transmits thefollowing permuted baseband signals from the two antennas:

$\begin{matrix}s_{1} & s_{2} & s_{3} & s_{4} & s_{5} & s_{6} & = & X_{1}^{T} \\{- s_{2}^{*}} & s_{1}^{*} & {- s_{4}^{*}} & s_{3}^{*} & {- s_{6}^{*}} & s_{5}^{*} & = & X_{2}^{T}\end{matrix}\quad$

The first antenna transmits the user symbols S₁, S₂, S₃, . . . astransmitted signal vector X₁ ^(T), the symbols transmitted in thecorrect order as would occur if only a single transmitting antenna werein use. Meanwhile, the second antenna element transmits the sequence−S₂*, S₁*, −S₄*, S₃*, . . . In other words every pair of symbols isreversed in order, the first symbol of the pair is sign reversed andboth symbols are complex-conjugated. The conventional method ofprocessing these symbols in the receiver is shown in FIG. 4 (describedbelow).

There are alternative sequences for arranging the transmitted STTD datato that (conventional) sequence provided above, which conventionalsequence works quite well with a standard CDMA RAKE receiver and a lowdispersion channel. Under high dispersion conditions, however, theconventional sequence works less well with both a RAKE receiver and anFFT equaliser receiver of the present invention. An improvement inrejection and equalisation can be obtained by rearrangement of the datathrough the substitution of symbol (i.e. code word) level coding by anequivalent chip level coding. If symbol S₁ has the chips C₁₁, C₁₂, . . .and symbol S₂ has the chips C₂₁, C₂₂, then the chip level STTD codingconsists of transmitting C₁₁, C₂₁, C₁₂, C₂₂, C₁₃, C₂₃, . . . from thefirst transmit antenna element and −C₂₁*, C₁₁*, −C₂₂*, C₁₂*, −C₂₃*,C₁₃*, . . . from the second transmit antenna number element. In otherwords, the pairs of code words forming the STTD transmission structureare split up and interleaved at the chip level. Similar changes must bereflected in the construction of the channel and user symbol matrices.This modified form of operation would impair the performance of a RAKEreceiver under high dispersion conditions, but improves the FFT-basedequaliser receiver of the preferred embodiment.

A set of matrices is now developed in order that the FFT method of thepresent invention can be applied to the exemplary STTD coding format.

To organise the received signal samples into a matrix formulation, letthe modulator data vector sequence {s₁, s₂, s₃, s₄, s₅ . . . } or itschip-level modification be X=X^(r)+jX^(i) and the permuted sequence{−s₂, s₁, −s₄, s₃, −s₆ . . . } be PX. P is a permutation and sign changematrix consisting of an identity matrix with some sign reversals andalternate columns exchanged. Eqn. (1) shows a permutation matrix which,when applied to the symbols radiated from the first antenna element,determine the symbols radiated from the second antenna element,

$\begin{matrix}{P = \begin{pmatrix}0 & {- 1} & \; & \; & \; & \; \\1 & 0 & \; & \; & \; & \; \\\; & \; & 0 & {- 1} & \; & \; \\\; & \; & {1\;} & 0 & \; & \; \\\; & \; & \; & \; & {0\;} & {- 1} \\\; & \; & \; & \; & 1 & 0\end{pmatrix}} & (1)\end{matrix}$

Let U be the complex signal radiated from the first antenna element andV that from the second antenna element. We have U=X, V=PX* For the realand imaginary parts of the received antenna signal Yin an ideal channel,we have

$\begin{matrix}{\begin{pmatrix}Y^{r} \\Y^{i}\end{pmatrix} = {{\begin{pmatrix}I & 0 & I & 0 \\0 & I & 0 & I\end{pmatrix}\;\begin{pmatrix}X^{r} \\X^{i} \\{PX}^{r} \\{- {PX}^{i}}\end{pmatrix}} = {\begin{pmatrix}{I + P} & 0 \\0 & {I - P}\end{pmatrix}\;\begin{pmatrix}X^{r} \\X^{i}\end{pmatrix}}}} & (2)\end{matrix}$

In words, Eqn. (2) shows how the permutation matrix is applied to thesymbols radiated from first element to determine the signals received atthe receiver antenna element with the contribution from the secondtransmit antenna element implicitly included. The real and imaginaryparts of the vectors are separate and stacked above each other in thisequation. Eqn. (2) initially assumes a perfect channel.

The channels from first and second antennas elements to the addressedsubscriber unit can be described by convolution matrices A₁=A₁ ^(r) ₊jA₁^(i). and correspondingly A₂=A₂ ^(r) ₊jA₂ ^(i). A convolution matrix isa Toeplitz matrix derived from the complex channel impulse response {h}such that if the data vector is D, the convolution of D with the channelimpulse response vector H is D©H=AD.

If

$\begin{matrix}{A = \begin{pmatrix}h_{0} & \; & \; & \; \\h_{1} & h_{0} & \; & \; \\h_{2} & h_{1} & h_{0} & \; \\\vdots & \; & \; & ⋰\end{pmatrix}} & (3)\end{matrix}$then

$\begin{matrix}\begin{matrix}{\begin{pmatrix}Y^{r} \\Y^{i}\end{pmatrix} = {\begin{pmatrix}A_{1}^{r} & {- A_{1}^{i}} & A_{2}^{r} & {- A_{2}^{i}} \\A_{1}^{i} & A_{1}^{r} & A_{2}^{i} & A_{r}^{r}\end{pmatrix}\;\begin{pmatrix}X^{r} \\X^{i} \\{PX}^{r} \\{- {PX}^{i}}\end{pmatrix}}} \\{= {\begin{pmatrix}\left( {A_{1}^{r} + {A_{2}^{r}P}} \right) & \left( {{- A_{1}^{i}} + {A_{2}^{i}P}} \right) \\\left( {A_{1}^{i} + {A_{2}^{i}P}} \right) & \left( {A_{1}^{r} - {A_{2}^{r}P}} \right)\end{pmatrix}\;\begin{pmatrix}X^{r} \\X^{i}\end{pmatrix}}}\end{matrix} & (4)\end{matrix}$

In words, Eqn. (3) next shows how the convolution matrix is defined andis, in fact, the matrixed valued variant of the ideal CIR vector. Thismatrix A contains the channel impulse response and is organised is sucha way that when it is multiplied into the transmitter sample vector theresultant vector is the received vector of samples with the distortionintroduced by the channel multi-path. Eqn. (4) shows how thisconvolution matrix is combined with the permutation matrix above to givethe vector of received samples when a two element STTD transmit antennais used. X^(r) and X^(i) are long vectors of the real and imaginaryparts. In other words, in Eqn. (4), knowing A, it is necessary toperform a convolution operation between two sequences, namely the CIRsequence A and the transmitted data sequence X to obtain the sequence ofreceived samples Y at the receive antenna element.

The imaginary samples can be interspersed with the real samples in thevectors X^(r), X^(i), Y^(r), Y^(i) as follows:

$\begin{matrix}{{\overset{\sim}{y} = {{\begin{pmatrix}Y_{1}^{r} \\Y_{1}^{i} \\Y_{2}^{r} \\Y_{2}^{i} \\\vdots\end{pmatrix}\mspace{40mu}\overset{\sim}{x}} = \begin{pmatrix}X_{1}^{r} \\X_{1}^{i} \\X_{2}^{r} \\X_{2}^{i} \\\vdots\end{pmatrix}}}\mspace{11mu}} & (5)\end{matrix}$

Putting this a different way, Eqn. (5) shows how the real and imaginaryparts of the transmitted and received and sample vectors are interleavedsuch that the real and imaginary parts of the samples appearalternately.

By performing corresponding row and column interchanges in the matrix A,a block circulant matrix in the equation {tilde over (y)}={tilde over(c)}{tilde over (x)} is obtained, provided the original channelconvolution matrices A₁ and A₂ were circulant.

Eqn. (6) shows how corresponding operations must be done on theconvolution matrix of Eqn. (4) to get the matrix {tilde over (c)}. Theprocess consists of row-by-row interleaving followed by column-by-columninterleaving (or vice-versa). The interleaved received sample vector{tilde over (y)} is now related to the interleaved transmitted vector{tilde over (x)} by the matrix product {tilde over (y)}={tilde over(c)}{tilde over (x)}. A typical 4×4 block of matrix {tilde over (c)} isas follows:

$\begin{matrix}\begin{pmatrix}\left( {A_{1}^{r} + {A_{2}^{r}P}} \right)_{k,k} & \left( {A_{1}^{r} + {A_{2}^{r}P}} \right)_{k,{k + 1}} & \left( {{- A_{1}^{i}} + {A_{2}^{i}P}} \right)_{k,k} & \left( {{- A_{1}^{i}} + {A_{2}^{i}P}} \right)_{k,{k + 1}} \\\left( {A_{1}^{r} + {A_{2}^{r}P}} \right)_{{k + 1},k} & \left( {A_{1}^{r} + {A_{2}^{r}P}} \right)_{{k + 1},{k + 1}} & \left( {{- A_{1}^{i}} + {A_{2}^{i}P}} \right)_{{k + 1},k} & \left( {{- A_{1}^{i}} + {A_{2}^{i}P}} \right)_{{k + 1},{k + 1}} \\\left( {A_{1}^{i} + {A_{2}^{i}P}} \right)_{k,k} & \left( {A_{1}^{i} + {A_{2}^{i}P}} \right)_{k,{k + 1}} & \left( {A_{1}^{r} - {A_{2}^{r}P}} \right)_{k,k} & \left( {A_{1}^{r} - {A_{2}^{r}P}} \right)_{k,{k + 1}} \\\left( {A_{1}^{i} + {A_{2}^{i}P}} \right)_{{k + 1},k} & \left( {A_{1}^{i} + {A_{2}^{i}P}} \right)_{{k + 1},{k + 1}} & \left( {A_{1}^{r} - {A_{2}^{r}P}} \right)_{{k + 1},k} & \left( {A_{1}^{r} - {A_{2}^{r}P}} \right)_{{k + 1},{k + 1}}\end{pmatrix} & (6)\end{matrix}$

Here the subscripts k,l refer to locations in the original matrices A₁^(r), A₁ ^(i) etc.

{tilde over (c)} is circulant but not block diagonal. By performing rowand column block Fourier transforms on this matrix it is converted toblock diagonal matrix {tilde over (C)} with 4×4 diagonal submatrices.Note that in this implementation the matrix equation (6) does notcorrespond to operations in the field of complex numbers and neither dothe block diagonal elements of {tilde over (C)} and therefore it is notpossible to write the elements of {tilde over (C)} as complex numbers.They remain as real-values entries corresponding to the separate realand imaginary parts.

In the case of a “least squares” solution, by adding thermal andreceiver noise to the antenna samples a Fourier domain equation of theform can be obtained. Eqn. (7) shows how the matrix product istransformed in to the frequency domain to enhance the computationefficiency and reduce DSP workload. A block Fourier transform is usedwhere, in this case, the blocks are of size 4. A block Fouriertransform, defined in [4] for example, consists of a number of parallelFFT operations performed on a vector of blocks in which thecorrespondingly located elements of each block are isolated and astandard FFT is performed thereon. Note that the block Fourier transformof the convolution matrix reduces it to a block diagonal form as shownin Eqn. (9).{tilde over (Y)}={tilde over (C)}{tilde over (X)}+W  (7)where Y is the block fourier transform (BFFT) of the vector y arrangedwith 4-length vector blocks, and W is a vector of uncorrelatedcomplex-valued Gaussian noise with covariance σ²I. This equation can besolved, with the standard least squares assumption, as{tilde over ({circumflex over (X)}=({tilde over (C)}^(H){tilde over(C)}+σ² I)⁻¹{tilde over (C)}^(H){tilde over (Y)}  (8)where (.)^(H) is an Hermitian transpose. The solution is numericallyefficient since it only involves inversion of the 4×4 sub-matrices, notthe whole matrix. Thus we assemble the left and right vector elementsinto groups of four and solve each group independently. Eqn. (8)therefore shows the desired least squares (LS) solution for thetransmitted symbols {tilde over (X)}; this is a standard form of thesolution readily appreciated by the skilled addressee. Since the matrixis now in block diagonal form, the computation count is very low.

$\begin{matrix}{\begin{pmatrix}{\hat{\overset{\sim}{X}}}_{1} \\{\hat{\overset{\sim}{X}}}_{2} \\{\hat{\overset{\sim}{X}}}_{3}\end{pmatrix} = {\begin{pmatrix}\left( {{{\overset{\sim}{C}}_{1}^{H}{\overset{\sim}{C}}_{1}} + {\sigma^{2}I}} \right)^{- 1} & \; & \; \\\; & \left( {{{\overset{\sim}{C}}_{2}^{H}{\overset{\sim}{C}}_{2}} + {\sigma^{2}I}} \right)^{- 1} & \; \\\; & \; & \left( {{{\overset{\sim}{C}}_{3}^{H}{\overset{\sim}{C}}_{3}} + {\sigma^{2}I}} \right)^{- 1}\end{pmatrix}\begin{pmatrix}{{\overset{\sim}{C}}_{1}^{H}{\overset{\sim}{Y}}_{1}} \\{{\overset{\sim}{C}}_{2}^{H}{\overset{\sim}{Y}}_{2}} \\{{\overset{\sim}{C}}_{3}^{H}{\overset{\sim}{Y}}_{3}}\end{pmatrix}}} & (9)\end{matrix}$

In the case of a direct FTT solution, the submatrices {tilde over(C)}_(m) of Eqn. (9) can be found directly by FFT operations on thechannel impulse responses. Letting these be h₁ ^(r)(k),h₁ ^(i)(k); h₂^(r)(k), h₂ ^(i)(k) k=0,1,2,3 . . . for the first and second downlinkchannels we have

$\begin{matrix}{A_{1}^{r} = \begin{pmatrix}{h_{1}^{r}(0)} & \; & \; & \; \\{h_{1}^{r}(1)} & {h_{1}^{r}(0)} & \; & \; \\{h_{1}^{r}(2)} & {h_{1}^{r}(1)} & {h_{1}^{r}(0)} & \; \\\vdots & \; & \; & ⋰\end{pmatrix}} & \text{(10a)} \\{{A_{1}^{r}P} = \begin{pmatrix}0 & {- {h_{1}^{r}(0)}} & \; & \; & \; \\{h_{1}^{r}(0)} & {- {h_{1}^{r}(1)}} & \; & \; & \; \\{h_{1}^{r}(1)} & {- {h_{1}^{r}(2)}} & 0 & {- {h_{1}^{r}(0)}} & \; \\{h_{1}^{r}(2)} & {- {h_{1}^{r}(3)}} & {h_{1}^{r}(0)} & {- {h_{1}^{r}(1)}} & \; \\\vdots & \; & \; & \; & ⋰\end{pmatrix}} & \text{(10b)} \\{{A_{2}^{i}P} = \begin{pmatrix}{h_{2}^{i}(0)} & \; & \; & \; \\{h_{2}^{i}(1)} & {h_{2}^{i}(0)} & \; & \; \\{h_{2}^{i}(2)} & {h_{2}^{i}(1)} & {h_{2}^{i}(0)} & \; \\\vdots & \; & \; & ⋰\end{pmatrix}} & \text{(10c)} \\{{A_{2}^{i}P} = \begin{pmatrix}0 & {- {h_{2}^{i}(0)}} & \; & \; & \; \\{h_{2}^{i}(0)} & {- {h_{2}^{i}(1)}} & \; & \; & \; \\{h_{2}^{i}(1)} & {- {h_{2}^{i}(2)}} & 0 & {- {h_{2}^{i}(0)}} & \; \\{h_{2}^{i}(2)} & {- {h_{2}^{i}(3)}} & {h_{2}^{i}(0)} & {- {h_{2}^{i}(1)}} & \; \\\vdots & \; & \; & \; & ⋰\end{pmatrix}} & \text{(10d)}\end{matrix}$

FIG. 5, with reference to Eqn. (6), shows the arrangement of elements inthe first column of the time domain circulant matrix {tilde over (c)}.

Block-vector Fourier transformation of this column yield the samediagonal blocks {tilde over (C)}_(m) of Eqn. (9).

$\begin{matrix}\left. \begin{pmatrix}{\overset{\sim}{c}}_{0} \\{\overset{\sim}{c}}_{1} \\{\overset{\sim}{c}}_{2} \\{\overset{\sim}{c}}_{3}\end{pmatrix}\Rightarrow{{Block}\mspace{14mu}{FFT}}\Rightarrow\begin{pmatrix}{\overset{\sim}{C}}_{0} \\{\overset{\sim}{C}}_{1} \\{\overset{\sim}{C}}_{2} \\{\overset{\sim}{C}}_{3}\end{pmatrix} \right. & (11)\end{matrix}$

To this point, conversion of the exemplary STTD block coding structureinto a corresponding matrix structure for Fourier analysis has occurred.Equations 12 to 14 illustrate that the physical convolution in themulti-path channel is mathematically defined by the FFT operation ofequation 14, i.e. the data is convolved in the multi-channel medium bythe CIR to give the samples in the time domain at multiple antennas.

In STTD applications, the DSP load is increased at the rate of 1 FFT perextra antenna. Hence, with use of the present invention, STTD andsimilar coding can be FFT equalised with about a two-fold to three-foldincrease in DSP load over an single transmit antenna system.

It is clear from this how to build up the matrix {tilde over (C)}directly from the channel impulse response samples. The associated dataand antenna samples for used with the column in FIG. 1 are as follows

$\begin{matrix}{{{Ant}.}:{\begin{pmatrix}{y_{1}^{r}(0)} \\{y_{1}^{i}(0)} \\{y_{2}^{r}(0)} \\{y_{2}^{i}(0)} \\{y_{1}^{r}(1)} \\{y_{1}^{i}(1)} \\\vdots\end{pmatrix}\mspace{25mu}{{Data}:\begin{pmatrix}{d^{r}(0)} \\{d^{i}(0)} \\{d^{r}(1)} \\{d_{i}^{i}(1)} \\\vdots\end{pmatrix}}}} & (12)\end{matrix}$

After forming the block DFT's of the vectors in this equation, the blockconvolution is equivalent to a point by point multiplication in theFourier Domain.Y _(2k) =H _(2k) D _(2k) +N _(2k) k=0 . . . L−1   (13)

The multiplication operation in Eqn. (13) is a matrix multiplication.The RAKE and joint detection algorithms in the Fourier domain are now

$\begin{matrix}{{\begin{matrix}{{\hat{D}}_{2k}^{M} = {H_{2k}^{H}Y_{2k}}} \\{{\hat{D}}_{2k}^{JD} = {\left( {{H_{2k}^{H}H_{2k}} + {\sigma^{2}I}} \right)H_{2k}^{H}Y_{2k}}}\end{matrix}\mspace{11mu} k} = {{0\;\ldots\; L} - 1}} & (14)\end{matrix}$

A terminal can use a plurality of receiving elements to enhancereception of the transmitted STTD signals. The straightforwardmodifications of the equations which allow this possibility are nowdescribed for a two element receiver array. In place of Eqn. (4) we have

$\begin{matrix}{\begin{pmatrix}Y_{1}^{r} \\Y_{1}^{i} \\Y_{2}^{r} \\Y_{2}^{i}\end{pmatrix} = {\begin{pmatrix}\left( {A_{11}^{r} + {A_{12}^{r}P}} \right) & \left( {{- A_{11}^{i}} + {A_{12}^{i}P}} \right) \\\left( {A_{11}^{i} + {A_{12}^{i}P}} \right) & \left( {A_{11}^{r} - {A_{12}^{r}P}} \right) \\\left( {A_{21}^{r} + {A_{21}^{r}P}} \right) & \left( {{- A_{21}^{i}} + {A_{22}^{i}P}} \right) \\\left( {A_{21}^{i} + {A_{22}^{i}P}} \right) & \left( {A_{21}^{r} - {A_{22}^{r}P}} \right)\end{pmatrix}\begin{pmatrix}X^{r} \\X^{i}\end{pmatrix}}} & (15)\end{matrix}$where Y₁ ^(r),Y₁ ^(i),Y₂ ^(r),Y₂ ^(i) are the real and imaginary partsof the sampled signals from the two antennas. Eqn. (15) now has matrixsize 8×4 blocks and in the Fourier domain the circulant {tilde over (C)}also has 8×4 blocks. In the least squares solution Eqn. (9) the matrixproduct {tilde over (C)}_(m) ^(H){tilde over (C)}_(m) remains at 4×4.The order of the matrices which must be inverted does not increase asthe number of diversity element increases though the “matched filter”product {tilde over (C)}_(m) ^(H){tilde over (Y)}_(m) does increase itsshare of the work load in proportion.

In the case of an FFT equaliser of the preferred embodiment, the channelimpulse response is written into the elements of a channel matrix, asexemplified in FIG. 5. Indeed, FIG. 5 is a time domain matrix of Eqn.(10), with the matrix developed from Eqn. 3 and Eqn. 4. FIG. 5 is anexemplary organisation of CIRs for a two element transmitter and asingle element receiver (of STTD), the matrix being suitable forprocessing by a block FFT. The matrix of FIG. 5 is therefore stored inmemory 150. Furthermore, as regards the CIRs within FIG. 5, CIRs havebeen separated into their real and imaginary parts, respectively, whilethe user data symbols and the receiving antenna signals are similarlyseparated out in a conformant fashion. The channel matrix can bemodified to a circulant matrix form such that an exact FFT method isapplicable.

With knowledge of the channel and conversion of received signals into amatrix supporting FFT processing, the FFT function can be performed onthe channel matrix, the user symbol matrix and the received data symbolssuch that the spectrum of the received signals is a linear combinationof the spectra of the signals transmitted from the two antennas. Inother words, at every frequency there is a linear matrix relationshipbetween the transmitted signals from the multiple transmit elements.Eqn. (15) can be solved for the transmitted user data symbolsindependently in each Fourier bin; this is a low complexity operationsince the matrices are small, typically 2×2 or 4×4. Finally, thespectrum of the estimated user symbols is inverse transformed into thetime domain to recover the data estimate, as previously described.

In the estimation of a work load, for an N-element receiving antenna werequire N FFT's of the received data samples on a block length which issomewhat larger than the packet size of the data. A 256-point FFT wouldbe suitable for a 192-chip data packet. The N channel impulse responsesmust also be FFT'ed. Every second input complex chip at the antennarequires the inversion of a 4×4 real matrix which takes a nominal 4³=64FLOP's (FLOP=floating point operation). After equalisation in theFourier domain the data is inverse FFT'ed.

By way of example, for a packet size of one hundred and ninety-twochips/bits (and allowing for sample shuffle overheads), the work isabout 2(N+1) 256-point FFT's plus ninety-six real matrix inversions oforder 4×4. For at two channel/element receiver, the computational countper sample is:6×256×log₂(256)+96×4³=18432 FLOPs

At an exemplary sample rate of 1.2288 mega-symbols per second (MS/s) anda packet repetition rate of 1228.8/192 (i.e. 6.4 kHz), the work rate forthe two channel/element receiver is therefore:6.400×18432=118 MFLOPs

The present invention has demonstrated that a joint detection algorithm,providing inter-code orthogonalisation and inter-symbol interferencereduction for an STTD coded transmission, is attainable and feasiblefrom a computation load criterion when performed in the Fourier domain.The present invention is not restricted to STTD techniques nor CDMAtechniques but also other types of digital receivers, including STCcoded systems having multiple blocks of data communicated to at leastone receive antenna element (and usually a plurality of receive antennaelements) from multiple transmit antenna elements and producing multipleoutput streams of data.

FIG. 6 shows the high level architecture of the wireless data system 600in which the present invention may be employed. The system 600 includesa router 602 providing access to the Internet 604 (or the like) from aserver 606 or subscriber station 608. The server may be coupled to therouter via an Ethernet connection 610. The router 602 supports aplurality of access points 612, 614 that provide wireless access to thesubscriber station 608 over high-speed data-links 616, 618. Thesubscriber station 608 may provide further access to a computer 620 viaan Ethernet or Infrared connection 622. The access points may themselvescontain multiple transmit elements to support the embodiments of FIG. 4.

The joint detection algorithm of the preferred embodiment can beimplemented in a self-contained integrated chip, as would be availablefrom a major semi-conductor manufacturer or a sub-routine can beinstalled into an ASIC chip. Use of the Fourier domain processingmechanism of the preferred embodiment (for channel impulse responsecorrection) greater reduces power consumption in a third generationsubscriber terminal.

Alternative embodiments of the invention may be implemented as computerprogram code encoded on a computer program product for use with acomputer system. It is expected that such a computer program product maybe distributed as a removable medium with accompanying printed orelectronic documentation (e.g. shrink-wrapped software), preloaded witha computer system or distributed from a server or electronic bulletinboard over a network (e.g. the Internet or World Wide Web). A series ofcomputer instructions can therefore either be fixed on a tangible mediumor fixed in a computer data signal embodied in a carrier wave that istransmittable to a computer system using wireline or wirelesstransmission techniques. The removable (i.e. tangible) medium may be acomputer readable media, such as a diskette, CD-ROM, DVD-ROM or RAM,fixed disk, magneto-optical disks, ROMs, flash memory or magnetic oroptical cards. The series of computer instructions embodies all or partof the functionality previously described herein with respect to thesystem.

Software embodiments are represented in FIG. 1 by a CD-ROM 70, theCD-ROM being shown as loadable into the exchange 12. Of course, insoftware based embodiments, requisite code may be required to bedownloaded into multiple physical entities, including the exchange andthe modem associated with the customer premises.

Software embodiments of the invention may be implemented in anyconventional computer programming language. For example, preferredembodiments may be implemented in a procedural programming language(e.g. “C”) or an object oriented programming language (e.g. “C++”).

Although the preferred operating method is realised by general orspecific-purpose processor or logic circuits programmed with suitablemachine-executable instructions, hardware components may possibly beused to implement certain features of the present invention. Of course,the present invention may be performed by a combination of hardware andsoftware.

It will, of course, be appreciated that the above description has beengiven by way of example only and that modifications in detail may bemade within the scope of the present invention. For example, while thepreferred embodiment has been described in the context of a CDMA system,the present invention is generally applicable to any dispersive orimperfect channel that acts to corrupt symbols, including systemsemploying TDD and FDM techniques and other types of links, such asdigital subscriber lines (DSL) and all digital transmission systems.Indeed, the matrix manipulation techniques of the preferred embodimentof the present invention (pertaining to multi-element transmissions andchannel equalization) can be applied to space-time coding (STC)techniques. In the context of the present invention, FFTs are thepreferred form of transform operation, although the skilled addresseewill appreciate that other equivalent forms of fast transform can beused, e.g. fast wavelet transforms. Consequently, the term FFT is notlimiting in the context of the present invention and the term “fasttransform” should be construed broadly to include, amongst other formsof transforms, both FFT and fast wavelet transforms, for example.

1. A method of channel equalisation comprising: receiving a data streamgenerated from a plurality of space time coded (STC) data streamsreceived from a plurality of transmit antenna elements; generating via afast transform a packet spectrum of at least a portion of the datastream, the packet spectrum being a transform domain representation;receiving a training sequence for a channel through which the datastream has been sent and assessing a channel impulse response for thechannel based on the training sequence; generating via a fast transforma channel impulse response spectrum in the transform domain for thechannel impulse response; equalising the packet spectrum with thechannel impulse response spectrum to produce an equalised packetspectrum in the transform domain; and converting the equalised packetspectrum into time domain equalised data for recovery of information. 2.The method of claim 1, wherein equalising the packet spectrum furtherincludes: deconvolving transmitted and received data streams withrespect to channel impulse response spectra, thereby to produce at leastone equalised data stream.
 3. The method of claim 1, wherein equalisingthe packet spectrum includes performing a minimum mean square error(MMSE) spectral ratio comparison.
 4. The method of claim 1, furthercomprising truncating the channel impulse response spectra to limitprocessing and enhance accuracy associated with equalising the packetspectrum.
 5. The method of claim 1, wherein assessing the channelimpulse response for the channel based on the training sequence furtherincludes assessing a matrix-valued channel impulse response.
 6. Themethod of claim 1, further comprising receiving the data stream at aplurality of receive antenna elements.
 7. The method of claim 1, whereinthe fast transform is a Fourier transform.
 8. The method of claim 1,wherein the data stream is distributed in slots across a plurality offrames, each slot including the training sequence.
 9. The method ofclaim 1, wherein the data stream is arranged such that a code-word levelconstruction of a Space Time Transmit Diversity (STTD) signal ismodified to a chip-level construction in which Code Division MultipleAccess (CDMA) code words are interleaved at a chip level instead ofbeing transmitted whole in sequence.
 10. The method of claim 1, whereinthe data stream is a slot of a data frame and the method furthercomprising reading the slot into memory.
 11. The method of claim 10,wherein said at least a portion of the data stream includes a packetoverlap.
 12. A computer program product for a processor of a channelequaliser, the computer program product comprising: code that supportsreception of a data stream generated from a plurality of space timecoded (STC) data streams received from a plurality of transmit antennaelements; code that generates via a fast transform a packet spectrum ofat least a portion of the data stream, the packet spectrum being atransform domain representation; code that supports reception of atraining sequence for a channel through which the data stream has beensent and code that assesses a channel impulse response for the channelbased on the training sequence; code that generates via a fast transforma channel impulse response spectrum in the transform domain for thechannel impulse response; code that equalizes the packet spectrum withthe channel impulse response spectrum to produce an equalised packetspectrum in the transform domain; and code that converts the equalizedpacket spectrum into time domain equalized data for recovery ofinformation; wherein the codes reside in a computer readable medium. 13.The computer program product of claim 12, further comprising: code thatdeconvolves transmitted and received data streams with respect tochannel impulse response spectra, thereby to produce at least oneequalised data stream, the code that deconvolves associated with thecode that equalizes the packet spectrum.
 14. The computer programproduct of claim 12, further comprising: code that assesses amatrix-valued channel impulse response, said code associated with thecode that assesses the channel impulse response for the channel based onthe training sequence.
 15. The computer program product of claim 12,further comprising: code that modifies a code-word level construction ofan Space Time Transmit Diversity (STTD) signal into a chip-levelconstruction in which Code Division Multiple Access (CDMA) code wordsare interleaved at a chip level instead of being transmitted whole insequence.
 16. An integrated chip having a controller programmed toprovide a channel equalisation function, the controller comprising: afirst receiver chain arranged, in use, to receive a data streamgenerated from a plurality of space time coded (STC) data streamsreceived from a plurality of transmit antenna elements; a first fasttransform function arranged to generate a packet spectrum of at least aportion of the data stream, the packet spectrum being a transform domainrepresentation; a second receiver chain arranged, in use, to receive atraining sequence for a channel through which the data stream has beensent; a channel impulse response estimator for assessing a channelimpulse response for the channel based on the training sequence; asecond fast transform function arranged to generate a channel impulseresponse spectrum in the transform domain for the channel impulseresponse; an equalizer arranged to equalise the packet spectrum with thechannel impulse response spectrum to produce an equalised packetspectrum in the transform domain; and an inverse transform functionarranged to convert the equalised packet spectrum into time domainequalised data for recovery of information.
 17. The integrated circuitof claim 16, wherein the equalizer further includes: a deconvolvingfunction arranged to deconvolve transmitted and received data streamswith respect to channel impulse response spectra, thereby to produce atleast one equalised data stream.
 18. An equaliser comprising: a firstinput for receiving a data stream generated from a plurality of spacetime coded (STC) data streams received from a plurality of transmitantenna elements; a processor arranged to select a sub-slot of data fromthe data stream and to implement a fast transform on the sub-slot togenerate a packet spectrum for the sub-slot of data, the packet spectrumbeing a transform domain representation; means for storing a channelimpulse response spectrum generated from a fast transform of a channelimpulse response of a channel through which the data stream has beensent, the channel impulse response spectrum being in the transformdomain; a least squares spectral ratio comparator coupled to receive thepacket spectrum and the channel impulse response spectrum, the leastspectral ratio comparator having an output providing an equalised packetspectrum in the transform domain; and means for converting the equalisedpacket spectrum into time domain equalised data for recovery ofinformation.
 19. The equaliser of claim 18, further includes: means fordeconvolving transmitted and received data streams with respect tochannel impulse response spectra, thereby to produce at least oneequalised data stream.
 20. The equaliser of claim 18, further comprisingmeans for truncating the channel impulse response spectra to limitprocessing and enhance accuracy associated with equalising the packetspectrum.
 21. The equaliser of claim 18, further comprising a memorystoring a matrix-valued channel impulse response.
 22. The equaliser ofclaim 18, the equaliser coupled to receive the data stream through aplurality of receive antenna elements.
 23. The equaliser of claim 18,wherein the first and second fast transforms are Fourier transforms. 24.The equaliser of claim 18, wherein the data stream includes the trainingsequence.
 25. The equaliser of claim 18, wherein the data stream isselected from a group comprising: STTD signals; transmit diversitysignals; and STC signals.
 26. A radio communication device comprisingthe equaliser having: a first input for receiving a data streamgenerated from a plurality of space time coded (STC) data streamsreceived from a plurality of transmit antenna elements; a processorarranged to select a sub-slot of data from the data stream and toimplement a fast transform on the sub-slot to generate a packet spectrumfor the sub-slot of data, the packet spectrum being a transform domainrepresentation; means for storing a channel impulse response spectrumgenerated from a fast transform of a channel impulse response of achannel through which the data stream has been sent, the channel impulseresponse spectrum being in the transform domain; a least squaresspectral ratio comparator coupled to receive the packet spectrum and thechannel impulse response spectrum, the least spectral ratio comparatorhaving an output providing an equalised packet spectrum in the transformdomain; and means for converting the equalised packet spectrum into timedomain equalised data for recovery of information.
 27. An equalisercomprising an input, a Random Access Memory (RAM) block, a RAM sampleblock, a spectrum ratio calculator having a first input connected to theRAM sample block and a second input connected to a RAM having an impulseresponse spectrum; wherein the equaliser is operable to: receive a datastream generated from a plurality of space time coded (STC) data streamsreceived from a plurality of transmit antenna elements; fill a RAMmemory block; converting the data stream by way of a fast Fouriertransform operation to provide a sample RAM block Y_(k) (packetspectrum) and providing the data stream to a first input of anequaliser; and receive, at a second input of the equaliser, an impulseresponse spectrum held within the RAM, which impulse response spectrumis a fast Fourier transform of the channel impulse response; thereby toequalise the data stream whereby to provide an equalised packet spectrumwhich undergoes an inverse fast Fourier transform to provide equalisedpacket waveforms.